Write the quadratic in standard form: (y = ax^2 + bx + c)
Identify the direction of opening:
(a > 0): opens upward
(a < 0): opens downward
Find the axis of symmetry using (x = frac{-b}{2a})
Find the vertex by substituting the axis of symmetry value into the equation
Find the y-intercept by setting (x = 0)
Find the x-intercepts by setting (y = 0) and solving the quadratic
Plot the vertex on the graph
Plot the axis of symmetry
Plot the y-intercept
Plot the x-intercepts if they exist
Choose additional points on both sides of the axis of symmetry
Reflect points across the axis of symmetry
Draw a smooth parabola through the plotted points